It is quite easy to see why hes unpopular, i asked a few friends, more casual types that do not sit on here like me browsing sherdog. They said Woodley complains to much and ostracizes a chunk of the UFC fan base (white people) by constantly complaining about racism and other excuses why he is not this huge star. People tend not to like complainers, especially in fighting. Even Mark Hunt got shit for complaining and hes ALWAYS been a fan favorite, and his complaining had nothing to do with race.
The reason they were put off by Woodleys comments, is they don't really buy that someone is trying to 'keep him down' or treat him a certain way because of the colour of his skin, to be frank a few of them said they would like him alot more if he just shut his mouth and tried to be an exciting fighter.
What's annoying is, when hes not crying and making excuses for his boring fight style (not pulling the trigger as a champion) I quite like him. When i see him on the Fox desk he seems honest and down to Earth and doesn't seem to put his bias into the conversation when talking to other fighters, even in his weightclass.